BoundaryIntegralEquations.jl

BoundaryIntegralEquations.jl provides the basis functionalities for implementing Boundary Element Methods. Currently, the package is focused on solving the Helmholtz equation for acoustical problems through the Kirchoff-Helmholtz integral Equation

\[\zeta(\mathbf{x})p(\mathbf{x}) + \int_\Gamma \frac{\partial G(\mathbf{x}, \mathbf{y})}{\partial \mathbf{n}(\mathbf{y})}p(\mathbf{y})\ \mathrm{d}S_\mathbf{y} - \mathrm{i} \rho_0 c k \int_\Gamma G(\mathbf{x},\mathbf{y})v_\mathbf{n}(\mathbf{y})\ \mathrm{d}S_\mathbf{y} = 0.\]

where

\[ G(\mathbf{x},\mathbf{y}) = \frac{\exp\left(\mathrm{i}k\|\mathbf{x} - \mathbf{y}\|_2\right)}{4\pi\|\mathbf{x} - \mathbf{y}\|_2},\]

is the Green's function of the Helmholtz operator, $k$ is the wavenumber, $\rho_0$ is the ambient density and $c$ is the speed of sound.

Mesh formats

• COMSOLs .mphtxt files (best for applying boundary conditions)
• .obj, .ply, .stl, .off, .2DM through MeshIO.jl.

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